It sold following a 10-minute battle between two rival bidders via telephone, after the price passed $70m.
The previous record for a living artist was American Jeff Koons's Balloon Dog sculptures, which went for £45.6 million in 2013.
Instead, he opted to sell without a reserve, a minimum price at which the work can be hammered down.
The painting led Christie's postwar and contemporary evening sale that totaled $357.2 million, within the estimated range. Hockney's sold his painting for $18,000 in 1972.More news: Sean 'Diddy' Combs' ex, Kim Porter, found dead at home
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It became the most celebrated of the artist's series of pool paintings, begun after he moved to California from the relative gloom of Bradford.
The painting was inspired by two photographs on the floor of Hockney's studio, one of the man standing and another of the swimmer. Hockney's 1972 work depicts a landscape reminiscent of the South of France containing two men including the artist's former lover Peter Schlesinger.
There is also sudden demand for the work of Hockney, who is 81.More news: Tech giants slide, pulling US stock market sharply lower
One of Hockney's most celebrated works, it has featured on the cover of a number of monographs about the artist and was part of an global retrospective that celebrated his 80th birthday in 2017.
The Hockney had been taken on tour to drive up potential buyer interest, in Hong Kong, London and Los Angeles.
With Christie's commission, "Portrait of an Artist (Pool with Two Figures)", surpassed the auction house's pre-sale estimate of about $80 million, according to Reuters.
"The strategy was new to everyone, including us", said Loic Gouzer, Christie's chairman of postwar and contemporary art.More news: Best Stan Lee Cameos From Marvel Movies!
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